Question

Which of the following represents the zeros of f(x) = x^3 – 2x^2 - 6x + 12?

Answer 1

The zeros of the function f(x) = x^3 - 2x^2 - 6x + 12 are found by factoring the polynomial and are x = 2, x = √6, and x = -√6.

Step-by-step explanation:

To find the zeros of the function f(x) = x^3 - 2x^2 - 6x + 12, we need to solve for x when f(x) = 0. This involves setting the equation x^3 - 2x^2 - 6x + 12 equal to zero and factoring or using other methods to solve for the values of x that satisfy the equation.

Let's try factoring by grouping:

1. Group the terms: (x^3 - 2x^2) - (6x - 12)
2. Factor out the common terms: x^2(x - 2) - 6(x - 2)
3. Since (x - 2) is common in both terms, factor it out: (x - 2)(x^2 - 6)
4. We now have a quadratic factor, which can be further factored: (x - 2)(x - √6)(x + √6)

Thus, the zeros of the function are x = 2, x = √6, and x = -√6. These are the values of x for which f(x) = 0.